It is shown that if S is a continuous linear operator in a Banach space which is a Grothendieck space with the Dunford-Pettis property, then \(S=\sum^{m}_{j=1}z_ jP_ j\) for some complex numbers \(z_ j\) and disjoint commuting projections \(P_ j\), \(1\leq j\leq m\), whose sum is the identity operator. The proof is based on the fact that in such Banach spaces a spectral measure can assume only finitely many values.